矩阵特征值的一类新的包含域

用盖尔圆盘定理来估计矩阵的特征值是一个经典的方法,这种方法仅利用矩阵的元素来确定特征值的分布区域.本文利用相似矩阵有相同的特征值这一理论,得到了矩阵特征值的一类新的包含域,它们与盖尔圆盘等方法结合起来能提高估计的精确度.     

Monitoring of the process of formation of epitaxial films with the use of ultrasoft x-ray spectroscopy

The distinctive features of the atomic and electronic structure of thin surface layers of substances in the process of formation of epitaxial silicon films on silicon are studied using the procedures of reflection and scattering of ultrasoft x-ray radiation. The angular distribution of the scattered x-ray radiation (the scattering indicatrices) and the near fine structure of SiL_2,3 spectra of reflection are investigated. The assumption of the sensitivity of the observed peak of anomalous scattering (the Yoneda peak) of x-ray radiation to the presence, in the surface regions of the materials, of extended double-boundary defects, the defects of packing, grain boundaries, dislocations, etc. is made. It is shown that the experimental procedure used makes it possible to obtain information on the surface layers of substances. Translated from Zhurnal Priklaldnoi Spektroskopii, Vol. 67, No. 4, pp. 496–498, July–August, 2000.     

THEORY AND COMPUTATION OF SECONDARY BIFURCATIONS NEAR A DOUBLE EIGENVALUE

This paper deals with secondary bifurcations near a double eigenvalue of a nonlinear equation with two parameters. Utilizing symmetries (or more generally, equivariances ) and introducing two new parameters, we give some extended systems so that the double singular points, secondary bifurcation points and initial secondary branches respectively become their regular solutions. The methods in this paper not only give more general conditions of secondary bifurcation but also avoid the adjacent singularities of existing extended systems for computing the simple bifurcation points on non-trivial solution branches A numerical example is presented, showing the effectiveness of our methods.     

Higgs bosons in the standard model,the MSSM and beyond

I summarize the basic theory and selected phenomenology for the Higgs boson(s) of the standard model, the minimal supersymmetric model and some extensions thereof, including the next-to-minimal supersymmetric model.     

Baeicklund Transformation and Multiple Soliton Solutions for （3＋1）-Dimensional Potential-YTSF Equation

We study an approach to constructing multiple soliton solutions of the (3 1)-dimensional nonlinear evolution equation. We take the (3 1)-dimensional potential- YTSF equation as an example. Using the extended homogeneous balance method, one can find a Backlund transformation to decompose the (3 1)-dimensional potential-YTSF equation into a set of partial differential equations. Starting from these partial differential equations, some multiple soliton solutions for the (3 1)-dimensional potential-YTSF equation are obtained by introducing a class of formal solutions.     

From Bowls to Capsules: Assembly of Hexanuclear NiII Rings Tailored by Alkali Cations

An anionic hexanuclear Ni^II metallamacrocycle with endo and exo linking sites has been employed as a building block to generate a series of capsules and bowls of nanometric size. The supramolecular arrangement of the {Ni₆} rings was tailored by the size of the alkali cations, showing the transition from {Ni₆-M₂-Ni₆} capsules (M=Li^I and Na^I) to {Ni₆-M} bowls (M=K^I and Cs^I). The alkyl co-cations are determinant to stabilize the assemblies by means of CH⋅⋅⋅π interactions on the exo side of the metallamacrocycles. The effect on the topology of the supramolecular assemblies of the cation size, cation charge, Et₃NH⁺ or Me₄N⁺ counter cations has been analyzed. Magnetic measurements reveal the presence of ferromagnetic and antiferromagnetic interactions inside the rings that allow a S=0 ground state.     

The extended Hulburt–Hirschfelder‐long‐range oscillator model for direct‐potential‐fit analysis

In the present work, an extended Hulburt–Hirschfelder oscillator model is proposed as a means of simplifying potential energy functions for direct‐potential‐fit analyses. The new potential energy function is joined smoothly to the long‐range inverse‐power dispersion energy expression. The new model is employed in direct‐potential‐fits using spectroscopic line positions that involve the ground electronic states of the principal isotopologues of hydrogen iodide and carbon monoxide, and the ground and first singlet‐sigma excited states of hydrogen fluoride and hydrogen chloride. The present methodology is found to lead to compact, flexible, and robust representations for the potential energy that compare favorably with the results of past work where more complicated models were employed.     

Quotient normed cones

Given a normed cone (X, p) and a subconeY, we construct and study the quotient normed cone (X/Y,p) generated byY. In particular we characterize the bicompleteness of (X/Y, ‖·‖ ^p ,p) in terms of the bicompleteness of (X, p), and prove that the dual quotient cone ((X/Y)^*, || · ‖·‖^p,p) can be identified as a distinguished subcone of the dual cone (X ^*, || · ||_{p, u}). Furthermore, some parts of the theory are presented in the general setting of the spaceCL(X, Y) of all continuous linear mappings from a normed cone (X, p) to a normed cone (Y, q), extending several well-known results related to open continuous linear mappings between normed linear spaces.     

Inequalities of Hadamard Type for r-Convex Functions in Carnot Groups

For a Carnot group G,we establish the relationship between extended mean values and r-convexfunctions which is introduced in this paper,which is a class of inequalities of Hadamard type for r-convexfunction on G.